It's not an easy task if you are seeking to be precise.
Illustrator won't do this easily. You'd have to manually draw the overall shapes and adjust perspective, size, and value for each element. A mesh in Illustrator fails because it's very difficult to get hard edge conversion areas, in addition, meshes distort the underlying objects based on position of mesh points. So, the overall pattern would look very different using a mesh.
The easiest way to do this is via displacement maps in Photoshop.
You create your basic document:
A layer of white objects and a solid black filled layer as a background.
You then create a grayscale document the same dimensions and add different values to create areas of depth.
The darker the area the farther off in the distance it will eventually be seen as. This is the difficult part. You probably have to play with the greyscale document to get it to accurately reflect the values for depth. This is called your Depth Map. When get it close save it as a standard greyscale .psd file somewhere you can locate easily.
Then going back to your set up file, choose
Filter > Distort > Displace. Click
OK in the first little window then an Open dialog will pop up. Select your greyscale .psd file at that point.
This will distort the layer in the set up file to match the depth map you created.
It just takes trial and error to get the depth map the way you want it.
There are a number of tutorials regarding this on the web if you search for them.
Then if you really need this in Illustrator I'd save and use Image Trace in Illustrator. Trying to create this in Illustrator alone would be a lesson is patience, if not frustration.